Adaptive design of experiment via normalizing flows for failure probability estimation

TL;DR

This paper introduces an adaptive experimental design method using normalizing flows and deep neural networks to efficiently estimate failure probabilities with expensive computer models, reducing simulation calls.

Contribution

It proposes a novel approach combining normalizing flows and DNNs for adaptive design in failure probability estimation, addressing computational expense.

Findings

Method reduces number of expensive computer model calls.

Normalizing flows effectively approximate the limit state posterior.

Proposed criteria improve design efficiency and accuracy.

Abstract

Failure probability estimation problem is an crucial task in engineering. In this work we consider this problem in the situation that the underlying computer models are extremely expensive, which often arises in the practice, and in this setting, reducing the calls of computer model is of essential importance. We formulate the problem of estimating the failure probability with expensive computer models as an sequential experimental design for the limit state (i.e., the failure boundary) and propose a series of efficient adaptive design criteria to solve the design of experiment (DOE). In particular, the proposed method employs the deep neural network (DNN) as the surrogate of limit state function for efficiently reducing the calls of expensive computer experiment. A map from the Gaussian distribution to the posterior approximation of the limit state is learned by the normalizing flows for the ease of experimental design. Three normalizing-flows-based design criteria are proposed in this work for deciding the design locations based on the different assumption of generalization error. The accuracy and performance of the proposed method is demonstrated by both theory and practical examples.